You have a converging (convex) lens and a diverging (concave) lens and the magnitude of the focal length of each lens is 38.5 cm.
(a) Determine which lens you should use in order to produce an image of a light bulb on a screen several metres away.
(b) Determine how far from the lens you should locate the screen in order to produce an image of the light bulb that is magnified by a factor of 2.10.
Yessss, can someone help pleaase??
(a) To produce an image of a light bulb on a screen several meters away, we should use a converging (convex) lens.
(b) To determine the distance from the lens to the screen in order to produce a magnified image, we can use the magnification formula:
Magnification (m) = -Image distance (di) / Object distance (do)
Given that the magnification (m) is 2.10, we can rearrange the formula to solve for the image distance (di).
di = -m * do
Given that the object distance (do) is the distance from the lens to the light bulb, we can substitute the known values and calculate:
do = 2 * focal length
Since the focal length of the lens is 38.5 cm, the object distance would be:
do = 2 * 38.5 cm = 77 cm
Now, plug in the values into the formula:
di = -2.10 * 77 cm ≈ -161.7 cm
Since the image distance is negative, it means the image is formed on the same side as the object (virtual image). The magnitude of the image distance is 161.7 cm.
Therefore, the screen should be located approximately 161.7 cm (or 1.617 meters) from the lens in order to produce a magnified image of the light bulb by a factor of 2.10.
To determine which lens to use and how far to place the screen for a desired image, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens,
- v is the image distance (distance of the image from the lens), and
- u is the object distance (distance of the object from the lens).
(a) To produce an image of a light bulb on a screen several meters away, we need to use a lens that forms a real image on the screen. For this, we need to use the diverging (concave) lens since it always forms a virtual image.
(b) Now, to determine how far from the lens we should place the screen in order to produce a magnified image with a magnification factor of 2.10, we need to use the lens formula again.
Given:
- Focal length of each lens (f) = 38.5 cm
We can rearrange the lens formula to solve for the image distance (v):
1/v = 1/f - 1/u
For a magnification factor (m) of 2.10, we have:
m = -v/u
Rearranging the terms, we get:
v = (-m) * u
Substituting the value of the magnification factor (m = 2.10) and the focal length (f = 38.5 cm), we can solve for the object distance (u):
u = -v / m = -v / 2.10
Now, we can substitute the value of u into the lens formula to calculate the image distance (v) and finally determine the screen distance.
Let's assume an object distance (u) of 1 meter (100 cm) for this example:
u = -100 cm
Substituting this into the lens formula:
1/f = 1/v - 1/u
1/38.5 = 1/v - 1/-100
Simplifying, we get:
1/v = 1/38.5 + 1/100
1/v = (100 + 38.5) / (38.5 * 100)
Now, solving for v:
v = 38.5 * 100 / (100 + 38.5)
v = 3850 / 138.5
v ≈ 27.8 cm
Therefore, for a magnified image with a factor of 2.10, the image distance (v) will be approximately 27.8 cm from the lens.